α-Gauss Curvature Flows with Flat Sides
2014.07.23 17:09
| 실적년도 | 2013년 |
|---|---|
| 논문구분 | 국외 |
| 총저자 | Lami Kim, Ki-Ahm Lee, Eunjai Rhee |
| 학술지명 | Journal of Differential Equations |
| 권(Vol.) | 254 |
| 호(No.) | 3 |
| 게재년월 | 2013년 1월 |
| Impact Factor | |
| SCI 등재 | SCI |
| 비고 |
In this paper, we study the deformation of the 2-dimensional convex surfaces in ℝ 3 whose speed at a point on the surface is proportional to α-power of positive part of Gauss Curvature. First, for 12<α≤1, we show that there is smooth solution if the initial data is smooth and strictly convex and that there is a viscosity solution with C 1,1-estimate before the collapsing time if the initial surface is only convex. Moreover, we show that there is a waiting time effect which means the flat spot of the convex surface will persist for a while. We also show the interface between the flat side and the strictly convex side of the surface remains smooth on 0<t<T 0 under certain necessary regularity and non-degeneracy initial conditions, where T 0 is the vanishing time of the flat side.
